October 1, 3:30pm, https://cmu.zoom.us/j/98951280265

Ting-Wei Chao, Carnegie Mellon University

Point sets in $\mathbb{R}^d$ without convex $k$-holes

Ting-Wei Chao, Carnegie Mellon University

Point sets in $\mathbb{R}^d$ without convex $k$-holes

Abstract:

Given a point set in $\mathbb{R}^d$ in general position, a convex $k$-hole is a $k$-element subset in convex position whose convex hull is empty inside. ErdÅ‘s and Szekeres proved that there always exists a $k$-element subset in convex position if the size of given point set is large enough. However, for k large enough, it's not guaranteed to be a $k$-hole. In this talk, I'll talk about the constructions of sets without $k$-holes.

Please email Boris Bukh (bbukh ~at~ math) for a **password**.